帮忙解决几道一元二次方程的题目！

1) x^2-√5*x+1/4=0

x1=(√5+2)/2, x2=(√5-2)/2

2) x^2-x=0

3) 4-4*6*a>=0

a<=1/6

x1+x2=-1/3，x1*x2=a/6

|x1-x2|=2

(x1-x2)^2=4

(x1+x2)^2-4x1*x2=4

1/9-4a/6=4

a=-35/6

4) b^2-4c>=0

b^2>=4c

(b,c)=(2,1)(3,1)(3,2)(4,1)(4,2)(4,3)(4,4)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

1+2+4+6+6=19

5) (1) 6x^2-3x-2=0两根为a，b

a+b=1/2，ab=-1/3

x1+x2=-1/a-1/b=-(a+b)/(ab)=3/2

x1*x2=(-1/a)(-1/b)=1/(ab)=-3

方程：x^2-3/2*x-3=0即 2x^2-3x-6=0

(2) 4x^2-3x-2=0两根为a，b

a+b=3/4，ab=-1/2

x1+x2=a^2+b^2=(a+b)^2-2ab=9/16+1=25/16

x1*x2=a^2*b^2=(ab)^2=1/4

方程：x^2-25/16*x+1/4=0即 16x^2-25x+4=0

6) x1+x2=(2m-1)/m，x1*x2=(m-2)/m

(x1-3)(x2-3)=5m

x1*x2-3(x1+x2)+9=5m

(m-2)/m-3(2m-1)/m+9=5m

(m-2)-3(2m-1)+9m=5m^2

5m^2-4m-1=0

(m-1)(5m+1)=0

m=1或m=-1/5(舍去)

7) 4(m+1)^2-4(4m+1)>=0 (1)

2(m+1)<0 (2)

4m+1<0 (3)

解得 m<-1

（累死了，以后少弄点题吧，遇上我这样的好心人算你的福气。希望能帮到你。祝学习进步！）